A conventional bicycle wheel is disclosed in FIG. 5 and generally includes a rim 50 to which a tire (not shown) is connected, and a plurality of spokes 60 are connected between the rim 50 and a hub (not shown) at the center of the wheel. The connection of the spoke 60 and the rim 50 is made by inserting a connection piece 70 in the rim 50 so that an end of the spoke 60 is threadedly connected to the connection piece 70. The spoke 60 is made of steel and has a diameter of 2 mm and the rim 50 has to be drilled a hole 51 of 4 mm for receiving the connection piece 70. In order to reduce the weight of the wheel, the latest spoke 60′ is made of aluminum alloy and has a diameter of 4 mm as shown in FIG. 6. In order to install the connection pieces 70, the holes 52 in the rim 50 have to be enlarged to 6 mm in diameter. The larger diameter of the holes are drilled, the less strength of the rim 50 will be. The rim bears the load of the bicycle frame and the weight of the cyclist, so that the size of the holes in the rim has to be reduced while the diameter of the spokes is kept being large enough. 
The present invention intends to provide a rim that includes holes with larger recess in an inner periphery of the rim so as to received an end of the spoke which is fixed to the rim by a screw from outer periphery of the rim.